Finite Group Databasebeta

← #61772

Subgroups — #61772

Order 256.

906 conjugacy classes of subgroups.

The subgroup lattice has 883 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3542C211yesmaximal, characteristic, complemented
2#3494C211yesmaximal, characteristic, complemented
3#3347C211yesmaximal, characteristic, complemented
4#3347C211yesmaximal, characteristic, complemented
5#3345C211yesmaximal, characteristic, complemented
6#3343C211yesmaximal, characteristic, complemented
7#3341C211yesmaximal, characteristic, complemented
8#3339C211yesmaximal, characteristic, complemented
9#3337C211yesmaximal, characteristic, complemented
10#3334C211yesmaximal, characteristic, complemented
11#3319C211yesmaximal, characteristic, complemented
12#3318C211yesmaximal, characteristic, complemented
13#3309C211yesmaximal, characteristic, complemented
14#3306C211yesmaximal, characteristic, complemented
15#3305C211yesmaximal, characteristic, complemented
16#3297C211yesmaximal, characteristic, complemented
17#3297C211yesmaximal, characteristic, complemented
18#3294C211yesmaximal, characteristic, complemented
19#3243C211yesmaximal, characteristic, complemented
20#3241C211yesmaximal, characteristic, complemented
21#3199C211yesmaximal, characteristic, complemented
22#3198C211yesmaximal, characteristic, complemented
23#3188C211yesmaximal, characteristic, complemented
24#3186C211yesmaximal, characteristic, complemented
25#3122C211yesmaximal, characteristic, complemented
26#3118C211yesmaximal, characteristic, complemented
27#3098C211yesmaximal, characteristic, complemented
28#3096C211yesmaximal, characteristic, complemented
29#3091C211yesmaximal, characteristic, complemented
30C2×#482C211yesmaximal, characteristic, complemented
31#2977C211yesmaximal, characteristic, complemented
32#562—21no—
33#560—21no—
34#555C2211yescharacteristic, complemented
35#555C2211yescharacteristic, complemented
36#555C2211yescharacteristic, complemented
37#553C2211yescharacteristic
38#553C2211yescharacteristic, complemented
39#553C2211yescharacteristic, complemented
40#553C2211yescharacteristic, complemented
41#553C2211yescharacteristic, complemented
42#552C2211yescharacteristic, complemented
43#551—21no—
44#551—21no—
45#551—21no—
46#550C2211yescharacteristic, complemented
47#547C2211yescharacteristic
48#547C2211yescharacteristic, complemented
49#547C2211yescharacteristic, complemented
50#546—21no—
51#546—21no—
52#546—21no—
53#546C2211yescharacteristic, complemented
54#546C2211yescharacteristic, complemented
55D42C2211yescharacteristic, complemented
56#544C2211yescharacteristic, complemented
57#542—21no—
58#542C2211yescharacteristic
59#540—21no—
60#540—21no—
61#540C2211yescharacteristic
62#538—21no—
63#537C2211yescharacteristic
64#535—21no—
65#535C2211yescharacteristic
66#535C2211yescharacteristic, complemented
67#534—21no—
68#532—21no—
69#529—21no—
70#525C2211yescharacteristic
71#525C2211yescharacteristic
72C2×#121C2211yescharacteristic
73C2×#121C2211yescharacteristic, complemented
74#520C2211yescharacteristic, complemented
75#518C2211yescharacteristic, complemented
76C2×#117C2211yescharacteristic, complemented
77#501C2211yescharacteristic, complemented
78#501C2211yescharacteristic, complemented
79#500C2211yescharacteristic, complemented
80#499C2211yescharacteristic, complemented
81#490C2211yescharacteristic, complemented
82#489C2211yescharacteristic, complemented
83#488C2211yescharacteristic, complemented
84#486C2211yescharacteristic, complemented
85#485C2211yescharacteristic, complemented
86#485C2211yescharacteristic, complemented
87#485C2211yescharacteristic, complemented
88#484C2211yescharacteristic, complemented
89#484C2211yescharacteristic, complemented
90#484C2211yescharacteristic, complemented
91#483C2211yescharacteristic, complemented
92#482C2211yescharacteristic
93#482C2211yescharacteristic
94#482C2211yescharacteristic, complemented
95#482C2211yescharacteristic, complemented
96#482C2211yescharacteristic, complemented
97#482C2211yescharacteristic, complemented
98#482C2211yescharacteristic, complemented
99#482C2211yescharacteristic, complemented
100#482C2211yescharacteristic, complemented
101#482C2211yescharacteristic, complemented
102#482C2211yescharacteristic, complemented
103#482C2211yescharacteristic, complemented
104#482C2211yescharacteristic, complemented
105#482C2211yescharacteristic, complemented
106#482C2211yescharacteristic, complemented
107#482C2211yescharacteristic, complemented
108#482C2211yescharacteristic, complemented
109#481C2211yescharacteristic, complemented
110#481C2211yescharacteristic, complemented
111#481C2211yescharacteristic, complemented
112#481C2211yescharacteristic, complemented
113#480C2211yescharacteristic
114#480C2211yescharacteristic, complemented
115#480C2211yescharacteristic, complemented
116#480C2211yescharacteristic, complemented
117#480C2211yescharacteristic, complemented
118#480C2211yescharacteristic, complemented
119#480C2211yescharacteristic, complemented
120#480C2211yescharacteristic, complemented
121#479C2211yescharacteristic, complemented
122#478C2211yescharacteristic, complemented
123#478C2211yescharacteristic, complemented
124#478C2211yescharacteristic, complemented
125#478C2211yescharacteristic, complemented
126#478C2211yescharacteristic, complemented
127#477C2211yescharacteristic, complemented
128#476C2211yescharacteristic, complemented
129#476C2211yescharacteristic, complemented
130#474C2211yescharacteristic, complemented
131#474C2211yescharacteristic, complemented
132#474C2211yescharacteristic, complemented
133#469C2211yescharacteristic, complemented
134#469C2211yescharacteristic, complemented
135#469C2211yescharacteristic, complemented
136#468C2211yescharacteristic, complemented
137#466C2211yescharacteristic
138#466C2211yescharacteristic
139#466C2211yescharacteristic
140#466C2211yescharacteristic
141#466C2211yescharacteristic, complemented
142#466C2211yescharacteristic, complemented
143#466C2211yescharacteristic, complemented
144#466C2211yescharacteristic, complemented
145#466C2211yescharacteristic, complemented
146#465C2211yescharacteristic, complemented
147#465C2211yescharacteristic, complemented
148#465C2211yescharacteristic, complemented
149#463C2211yescharacteristic, complemented
150#463C2211yescharacteristic, complemented
151#459C2211yescharacteristic, complemented
152#459C2211yescharacteristic, complemented
153#450C2211yescharacteristic, complemented
154#449C2211yescharacteristic, complemented
155#449C2211yescharacteristic, complemented
156#449C2211yescharacteristic, complemented
157#449C2211yescharacteristic, complemented
158#447C2211yescharacteristic
159#447C2211yescharacteristic
160#447C2211yescharacteristic
161#447C2211yescharacteristic, complemented
162#447C2211yescharacteristic, complemented
163#447C2211yescharacteristic, complemented
164#447C2211yescharacteristic, complemented
165#442C2211yescharacteristic, complemented
166#442C2211yescharacteristic, complemented
167#442C2211yescharacteristic, complemented
168#440C2211yescharacteristic, complemented
169C4×SD16C2211yescharacteristic, complemented
170C4×D8C2211yescharacteristic, complemented
171C4×D8C2211yescharacteristic, complemented
172C4×D8C2211yescharacteristic, complemented
173#435C2211yescharacteristic, complemented
174#435C2211yescharacteristic, complemented
175#435C2211yescharacteristic, complemented
176#435C2211yescharacteristic, complemented
177C8×D4C2211yescharacteristic, complemented
178C8×D4C2211yescharacteristic, complemented
179C8×D4C2211yescharacteristic, complemented
180C8×D4C2211yescharacteristic, complemented
181#433C2211yescharacteristic, complemented
182#433C2211yescharacteristic, complemented
183#428C2211yescharacteristic, complemented
184#428C2211yescharacteristic, complemented
185#427C2211yescharacteristic, complemented
186#427C2211yescharacteristic, complemented
187#427C2211yescharacteristic, complemented
188C2×#107C2211yescharacteristic, complemented
189C2×#107C2211yescharacteristic, complemented
190C2×#106C2211yescharacteristic, complemented
191#418C2211yescharacteristic, complemented
192#417C2211yescharacteristic, complemented
193#416C2211yescharacteristic, complemented
194#416C2211yescharacteristic, complemented
195#416C2211yescharacteristic, complemented
196C2×#102C2211yescharacteristic, complemented
197C2×#102C2211yescharacteristic, complemented
198C2×#102C2211yescharacteristic, complemented
199#408C2211yescharacteristic, complemented
200#408C2211yescharacteristic, complemented
201C2×C22⋊C8C2211yescharacteristic, complemented
202C2×C22⋊C8C2211yescharacteristic, complemented
203C2×#41—21no—
204C2×#41—21no—
205C2×#41—21no—
206C2×#41C2311yescharacteristic
207C2×#41C2311yescharacteristic
208C2×#41C2311yescharacteristic
209C22×D4—21no—
210C22×D4—21no—
211C22×D4—21no—
212C22×D4C2311yescharacteristic
213C22×D4C2311yescharacteristic
214C22×D4C2311yescharacteristic
215C23×C4C2311yescharacteristic
216C2×SD16C2311yescharacteristic
217C2×SD16C2311yescharacteristic
218C2×D8C2311yescharacteristic
219C2×D8C2311yescharacteristic
220C2×D8C2311yescharacteristic
221C2×D8C2311yescharacteristic
222C2×D8C2311yescharacteristic
223C2×D8C2311yescharacteristic
224C2×M16C2311yescharacteristic
225C2×M16C2311yescharacteristic
226C22×C8C2311yescharacteristic
227C22×C8C2311yescharacteristic
228C22×C8C2311yescharacteristic
229C22×C8C2311yescharacteristic
230C22×C8C2311yescharacteristic
231C22×C8C2311yescharacteristic
232C4⋊Q8—21no—
233C4⋊Q8C2311yescharacteristic
234C4⋊Q8C2311yescharacteristic
235C4⋊Q8C2311yescharacteristic
236#127—21no—
237#127—21no—
238#127—21no—
239#127C2311yescharacteristic
240#126—21no—
241#126—21no—
242#126—21no—
243#126—21no—
244#126—21no—
245#126—21no—
246#126—21no—
247#125—21no—
248#125—21no—
249#125C2311yescharacteristic
250#125C2311yescharacteristic
251#125C2311yescharacteristic
252#124—21no—
253#124—21no—
254#124—21no—
255#124—21no—
256#124—21no—
257#124—21no—
258#124—21no—
259#124—21no—
260#124—21no—
261#124C2311yescharacteristic
262#123—21no—
263#123—21no—
264#123—21no—
265#123—21no—
266#123—21no—
267#123—21no—
268#123—21no—
269#123—21no—
270#123—21no—
271#123—21no—
272#123—21no—
273#123—21no—
274#123—21no—
275#123—21no—
276#123—21no—
277#123—21no—
278#123—21no—
279#123—21no—
280#123D411yescharacteristic
281#123D411yescharacteristic
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—21no—
289C22⋊Q8D411yescharacteristic
290C22⋊Q8D411yescharacteristic
291C22⋊Q8C2311yescharacteristic
292C22⋊Q8C2311yescharacteristic
293C22⋊Q8C2311yescharacteristic
294#121—21no—
295#121—21no—
296#121—21no—
297#121—21no—
298#121—21no—
299#121—21no—
300#121—21no—
301#121—21no—
302#121—21no—
303#121—21no—
304#121—21no—
305#121—21no—
306#121—21no—
307#121—21no—
308#121—21no—
309#121—21no—
310#121—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121—21no—
316#121D411yescharacteristic
317#121D411yescharacteristic
318#121C2311yescharacteristic
319#121C2311yescharacteristic
320#121C2311yescharacteristic
321#121C2311yescharacteristic
322#121C2311yescharacteristic
323#121C2311yescharacteristic
324#121C2311yescharacteristic
325#121C2311yescharacteristic
326#121C2311yescharacteristic
327#121C2311yescharacteristic
328#121C2311yescharacteristic
329#121C2311yescharacteristic
330#121C2311yescharacteristic
331#121C2311yescharacteristic
332#121C2311yescharacteristic
333#121C2311yescharacteristic
334#121C2311yescharacteristic
335#120—21no—
336#120—21no—
337#120—21no—
338#120—21no—
339#120—21no—
340#120—21no—
341#120—21no—
342#120—21no—
343#120—21no—
344#120D411yescharacteristic
345#120D411yescharacteristic
346C4×Q8—21no—
347C4×Q8C2311yescharacteristic
348C4×D4—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4—21no—
353C4×D4—21no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—21no—
357C4×D4—21no—
358C4×D4—21no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4C2311yescharacteristic
362C4×D4C2311yescharacteristic
363C4×D4C2311yescharacteristic
364C4×D4C2311yescharacteristic
365C4×D4C2311yescharacteristic
366C4×D4C2311yescharacteristic
367C4×D4C2311yescharacteristic
368C4×D4C2311yescharacteristic
369C4×D4C2311yescharacteristic
370C4×D4C2311yescharacteristic
371C4×D4C2311yescharacteristic
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#117—21no—
378#117C2311yescharacteristic
379#117C2311yescharacteristic
380#117C2311yescharacteristic
381#117C2311yescharacteristic
382#117C2311yescharacteristic
383#117C2311yescharacteristic
384#117C2311yescharacteristic
385#117C2311yescharacteristic
386#117C2311yescharacteristic
387C2×C4⋊C4C2311yescharacteristic
388C2×C4⋊C4C2311yescharacteristic
389C2×C4⋊C4C2311yescharacteristic
390C2×C4⋊C4C2311yescharacteristic
391C2×C4⋊C4C2311yescharacteristic
392C2×C4⋊C4C2311yescharacteristic
393C2×C4⋊C4C2311yescharacteristic
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C42—21no—
402#107C2311yescharacteristic
403#107C2311yescharacteristic
404#107C2311yescharacteristic
405#107C2311yescharacteristic
406#107C2311yescharacteristic
407#107C2311yescharacteristic
408#107C2311yescharacteristic
409#107C2311yescharacteristic
410#107C2311yescharacteristic
411#107C2311yescharacteristic
412#107C2311yescharacteristic
413#107C2311yescharacteristic
414#107C2311yescharacteristic
415#107C2311yescharacteristic
416#106C2311yescharacteristic
417#106C2311yescharacteristic
418#106C2311yescharacteristic
419#106C2311yescharacteristic
420#106C2311yescharacteristic
421#106C2311yescharacteristic
422#106C2311yescharacteristic
423#106C2311yescharacteristic
424#106C2311yescharacteristic
425#106C2311yescharacteristic
426C4⋊C8C2311yescharacteristic
427C4⋊C8C2311yescharacteristic
428C4⋊C8C2311yescharacteristic
429C4⋊C8C2311yescharacteristic
430#103C2311yescharacteristic
431#103C2311yescharacteristic
432#103C2311yescharacteristic
433#103C2311yescharacteristic
434#103C2311yescharacteristic
435#103C2311yescharacteristic
436#102C2311yescharacteristic
437#102C2311yescharacteristic
438#102C2311yescharacteristic
439#102C2311yescharacteristic
440#102C2311yescharacteristic
441#102C2311yescharacteristic
442#102C2311yescharacteristic
443#102C2311yescharacteristic
444#102C2311yescharacteristic
445#102C2311yescharacteristic
446#102C2311yescharacteristic
447#102C2311yescharacteristic
448#102C2311yescharacteristic
449#102C2311yescharacteristic
450#102C2311yescharacteristic
451#102C2311yescharacteristic
452#102C2311yescharacteristic
453#102C2311yescharacteristic
454#102C2311yescharacteristic
455#102C2311yescharacteristic
456#102C2311yescharacteristic
457#102C2311yescharacteristic
458#102C2311yescharacteristic
459#102C2311yescharacteristic
460#102C2311yescharacteristic
461#102C2311yescharacteristic
462C22⋊C8C2311yescharacteristic
463C22⋊C8C2311yescharacteristic
464C22⋊C8C2311yescharacteristic
465C22⋊C8C2311yescharacteristic
466C22⋊C8C2311yescharacteristic
467C22⋊C8C2311yescharacteristic
468C22⋊C8C2311yescharacteristic
469C22⋊C8C2311yescharacteristic
470C22⋊C8C2311yescharacteristic
471C22⋊C8C2311yescharacteristic
472C22⋊C8C2311yescharacteristic
473C22⋊C8C2311yescharacteristic
474#97C2311yescharacteristic
475#97C2311yescharacteristic
476C4×C8C2311yescharacteristic
477C4×C8C2311yescharacteristic
478C24—21no—
479C24—21no—
480C24—21no—
481C24C2×D411yescharacteristic
482#41—41no—
483#41—41no—
484#41—41no—
485#41—41no—
486#41—41no—
487#41—41no—
488#41—82no—
489#41—82no—
490#41—82no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8C2×D411yescharacteristic
495C2×Q8C2411yescharacteristic
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4—41no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—41no—
526C2×D4—82no—
527C2×D4—82no—
528C2×D4—82no—
529C2×D4C2×D411yescharacteristic
530C2×D4C2×D411yescharacteristic
531C2×D4C2×D411yescharacteristic
532C2×D4C2×D411yescharacteristic
533C2×D4C2×D411yescharacteristic
534C2×D4C2×D411yescharacteristic
535C2×D4C2×D411yescharacteristic
536C2×D4C2411yescharacteristic
537C2×D4C2411yescharacteristic
538C2×D4C2411yescharacteristic
539C2×D4C2411yescharacteristic
540C2×D4C2411yescharacteristic
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—41no—
558C22×C4—41no—
559C22×C4C2×D411yescharacteristic
560C22×C4C2×D411yescharacteristic
561C22×C4C2×D411yescharacteristic
562C22×C4C2411yescharacteristic
563C22×C4C2411yescharacteristic
564C22×C4C2411yescharacteristic
565C22×C4C2411yescharacteristic
566C22×C4C2411yescharacteristic
567SD16—41no—
568SD16—41no—
569D8—41no—
570D8—41no—
571D8—41no—
572D8—41no—
573D8—41no—
574D8—41no—
575M16—41no—
576M16—41no—
577C2×C8—41no—
578C2×C8—41no—
579C2×C8—41no—
580C2×C8—41no—
581C2×C8—41no—
582C2×C8—41no—
583C2×C8C2411yescharacteristic
584C2×C8C2411yescharacteristic
585C2×C8C2411yescharacteristic
586C2×C8C2411yescharacteristic
587C2×C8C2411yescharacteristic
588C2×C8C2411yescharacteristic
589C2×C8C2411yescharacteristic
590C2×C8C2411yescharacteristic
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4C2×D411yescharacteristic
612C4⋊C4C2×D411yescharacteristic
613C4⋊C4C2×D411yescharacteristic
614C4⋊C4C2×D411yescharacteristic
615C4⋊C4C2×D411yescharacteristic
616C4⋊C4C2×D411yescharacteristic
617C4⋊C4C2411yescharacteristic
618C4⋊C4C2411yescharacteristic
619C4⋊C4C2411yescharacteristic
620C4⋊C4C2411yescharacteristic
621C4⋊C4C2411yescharacteristic
622C4⋊C4C2411yescharacteristic
623C4⋊C4C2411yescharacteristic
624C4⋊C4C2411yescharacteristic
625C4⋊C4C2411yescharacteristic
626C4⋊C4C2411yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4C2×D411yescharacteristic
665C22⋊C4C2×D411yescharacteristic
666C22⋊C4C2×D411yescharacteristic
667C22⋊C4C2×D411yescharacteristic
668C22⋊C4C2×D411yescharacteristic
669C22⋊C4C2×D411yescharacteristic
670C22⋊C4C2×D411yescharacteristic
671C22⋊C4C2×D411yescharacteristic
672C22⋊C4C2×D411yescharacteristic
673C22⋊C4C2×D411yescharacteristic
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42C2411yescharacteristic
684C42C2411yescharacteristic
685C23—22no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—41no—
692C23—41no—
693C23—42no—
694C23—42no—
695C23—81no—
696C23—81no—
697C23—81no—
698C23—81no—
699C23—81no—
700C23—81no—
701C23—81no—
702C23C22×D411yescharacteristic
703C23C22×D411yescharacteristic
704C23C22×D411yescharacteristic
705C23C22×D411yescharacteristic
706C23C22×D411yescharacteristic
707Q8—21no—
708Q8—21no—
709Q8—41no—
710Q8—81no—
711Q8—81no—
712Q8—81no—
713D4—22no—
714D4—22no—
715D4—21no—
716D4—21no—
717D4—21no—
718D4—21no—
719D4—21no—
720D4—21no—
721D4—21no—
722D4—21no—
723D4—21no—
724D4—21no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—42no—
734D4—81no—
735D4—81no—
736D4—81no—
737D4—81no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752D4—81no—
753D4—81no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—81no—
781C2×C4—81no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4—81no—
788C2×C4—81no—
789C2×C4—81no—
790C2×C4—81no—
791C2×C4—81no—
792C2×C4—81no—
793C2×C4—81no—
794C2×C4C22×D411yescharacteristic
795C2×C4C22×D411yescharacteristic
796C2×C4C22×D411yescharacteristic
797C2×C4C22×D411yescharacteristic
798C2×C4C22×D411yescharacteristic
799C2×C4C22×D411yescharacteristic
800C2×C4C22×D411yescharacteristic
801C2×C4C22×D411yescharacteristic
802C2×C4C22×D411yescharacteristic
803C2×C4C2511yescharacteristic
804C8—21no—
805C8—21no—
806C8—21no—
807C8—21no—
808C8—21no—
809C8—21no—
810C8—21no—
811C8—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—82no—
842C22—162no—
843C22—162no—
844C22—162no—
845C22#57612yes—
846C22C23×D411yescharacteristic
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4#58511yescharacteristic
868C4#58511yescharacteristic
869C2—22no—
870C2—41no—
871C2—41no—
872C2—41no—
873C2—41no—
874C2—81no—
875C2—81no—
876C2—81no—
877C2—81no—
878C2—81no—
879C2#348511yescharacteristic
880C2C2×#57611yescharacteristic
881C2#358411yescharacteristic
subgroupG/H
center, socleC22C23×D4
commutator, Frattini, cosocleC2×C4C25
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ #525 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3542C2semidirect
2. #3494C2semidirect
3. #3347C2semidirect
4. #3347C2semidirect
5. #3345C2semidirect
6. #3343C2semidirect
7. #3341C2semidirect
8. #3339C2semidirect
9. #3337C2semidirect
10. #3334C2semidirect
11. #3319C2semidirect
12. #3318C2semidirect
13. #3309C2semidirect
14. #3306C2semidirect
15. #3305C2semidirect
16. #3297C2semidirect
17. #3297C2semidirect
18. #3294C2semidirect
19. #3243C2semidirect
20. #3241C2semidirect
21. #3199C2semidirect
22. #3198C2semidirect
23. #3188C2semidirect
24. #3186C2semidirect
25. #3122C2semidirect
26. #3118C2semidirect
27. #3098C2semidirect
28. #3096C2semidirect
29. #3091C2semidirect
30. C2×#482C2semidirect
31. #2977C2semidirect
34. #555C22semidirect
35. #555C22semidirect
36. #555C22semidirect
38. #553C22semidirect
39. #553C22semidirect
40. #553C22semidirect
41. #553C22semidirect
42. #552C22semidirect
46. #550C22semidirect
48. #547C22semidirect
49. #547C22semidirect
53. #546C22semidirect
54. #546C22semidirect
55. D42C22semidirect
56. #544C22semidirect
66. #535C22semidirect
73. C2×#121C22semidirect
74. #520C22semidirect
75. #518C22semidirect
76. C2×#117C22semidirect
77. #501C22semidirect
78. #501C22semidirect
79. #500C22semidirect
80. #499C22semidirect
81. #490C22semidirect
82. #489C22semidirect
83. #488C22semidirect
84. #486C22semidirect
85. #485C22semidirect
86. #485C22semidirect
87. #485C22semidirect
88. #484C22semidirect
89. #484C22semidirect
90. #484C22semidirect
91. #483C22semidirect
94. #482C22semidirect
95. #482C22semidirect
96. #482C22semidirect
97. #482C22semidirect
98. #482C22semidirect
99. #482C22semidirect
100. #482C22semidirect
101. #482C22semidirect
102. #482C22semidirect
103. #482C22semidirect
104. #482C22semidirect
105. #482C22semidirect
106. #482C22semidirect
107. #482C22semidirect
108. #482C22semidirect
109. #481C22semidirect
110. #481C22semidirect
111. #481C22semidirect
112. #481C22semidirect
114. #480C22semidirect
115. #480C22semidirect
116. #480C22semidirect
117. #480C22semidirect
118. #480C22semidirect
119. #480C22semidirect
120. #480C22semidirect
121. #479C22semidirect
122. #478C22semidirect
123. #478C22semidirect
124. #478C22semidirect
125. #478C22semidirect
126. #478C22semidirect
127. #477C22semidirect
128. #476C22semidirect
129. #476C22semidirect
130. #474C22semidirect
131. #474C22semidirect
132. #474C22semidirect
133. #469C22semidirect
134. #469C22semidirect
135. #469C22semidirect
136. #468C22semidirect
141. #466C22semidirect
142. #466C22semidirect
143. #466C22semidirect
144. #466C22semidirect
145. #466C22semidirect
146. #465C22semidirect
147. #465C22semidirect
148. #465C22semidirect
149. #463C22semidirect
150. #463C22semidirect
151. #459C22semidirect
152. #459C22semidirect
153. #450C22semidirect
154. #449C22semidirect
155. #449C22semidirect
156. #449C22semidirect
157. #449C22semidirect
161. #447C22semidirect
162. #447C22semidirect
163. #447C22semidirect
164. #447C22semidirect
165. #442C22semidirect
166. #442C22semidirect
167. #442C22semidirect
168. #440C22semidirect
169. C4×SD16C22semidirect
170. C4×D8C22semidirect
171. C4×D8C22semidirect
172. C4×D8C22semidirect
173. #435C22semidirect
174. #435C22semidirect
175. #435C22semidirect
176. #435C22semidirect
177. C8×D4C22semidirect
178. C8×D4C22semidirect
179. C8×D4C22semidirect
180. C8×D4C22semidirect
181. #433C22semidirect
182. #433C22semidirect
183. #428C22semidirect
184. #428C22semidirect
185. #427C22semidirect
186. #427C22semidirect
187. #427C22semidirect
188. C2×#107C22semidirect
189. C2×#107C22semidirect
190. C2×#106C22semidirect
191. #418C22semidirect
192. #417C22semidirect
193. #416C22semidirect
194. #416C22semidirect
195. #416C22semidirect
196. C2×#102C22semidirect
197. C2×#102C22semidirect
198. C2×#102C22semidirect
199. #408C22semidirect
200. #408C22semidirect
201. C2×C22⋊C8C22semidirect
202. C2×C22⋊C8C22semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#35422
#34942
#33472
#33452
#33432
#33412
#33392
#33372
#33342
#33192
#33182
#33092
#33062
#33052
#32972
#32942
#32432
#32412
#31992
#31982
#31882
#31862
#31222
#31182
#30982
#30962
#30912
C2×#4822
#29772